Question

The surface area of a cube is 18 3/8 m square. Find its volume.

Answer 1

Answer:

$5\frac{23}{64}\approx 5.36$ cubic meters.

Step-by-step explanation:

We have been given that the surface area of a cube is $18\frac{3}{8}$ square meters and we are asked to find the volume of the cube.

Since we know that surface area of a cube with each edge equals a units is:

$\text{Total surface area of cube}=6a^2$

Let us find length of each edge using surface area formula.

$18\frac{3}{8}=6a^2$

Let us convert our given area into mixed fraction.

$\frac{147}{8}=6a^2$

Upon dividing both sides of our equation by 6 we will get,

$\frac{147}{8*6}=a^2$

$\frac{147}{48}=a^2$  

Upon taking square root of both sides we will get,

$\frac{7\sqrt{3}}{4\sqrt{3}}=a$  

$\frac{7}{4}=a$

Now we will use volume of cube formula with each side length 'a'.

$\text{Volume of cube}=a^3$

$\text{Volume of cube}=(\frac{7}{4})^3$

$\text{Volume of cube}=\frac{343}{64}$

$\text{Volume of cube}=5\frac{23}{64}$

$\text{Volume of cube}=5.359375\approx 5.36$

Therefore, the volume of cube will be $5\frac{23}{64}$ cubic meters.